In Logic, how do I “collect” all used audio files into one folder?

Actually there are two features (both to be found in the Audio window’s Audio File menu):
Move audiofiles: This will do exactly what it says, it moves (i.e. copies and then deletes originals) all selected files to a directory which you then might specify. Pick “Select used” from the Audio window’s Edit menu, and then pick “Move” from the Audio File menu.
Copy/Convert audiofiles: This will create copies of all selected files, again you might specify the directory.

Use the move function only as long as you’re sure about not using the selected files in another song as well (Logic won’t find them then), otherwise better use the copy function. If you want to avoid any kind of problems, you might try the following:
Select all used regions in the Arrange window. In the Arrange window’s Audio menu, pick “Convert regions to individual audiofiles”. This might take a while. Logic asks you for a directory. Choose the one for your song, or better, create a new one, since you might want to clean up your HD a bit after all those actions.
Go into the Audio window, choose “Select unused” from the Audio menu, and just press “DEL” (or backspace) instead of using “delete audiofiles”. That way they will just be deleted from Logic’s audio window, not from your HD. Now you will have a “clean” song folder which contains a file for every region your song uses.
Once you’re done with these steps you might want to delete all the redundant wave files (as long as they’re not used by some other song of course). Should be safe now.

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